Knowledge, belief and time (Q1104923)

A logical system with a language including \(K_ ia\) (i knows a), \(B_ ia\) (i believes a), \({\mathcal K}a\) (common knowledge of a), \({\mathcal B}a\) (common belief of a) is proposed. Possible world semantics with 2 binary relations for each person i, 17 axioms and 2 rules is given. For the logic thus syntactically determined a completeness result is proved. Different notions of belief are distinguished. The logic is extended to capture time by adding the modal operators next, always, until to the language.